Quadratic Formula Program, QUAD2, on the TI-86 (85)

The web page 208607.htm presents and describes a program, QUAD1, that performs the "quadratic formula" for solving certain quadratic equations of the form

Ax² + Bx + C = 0 where we are assuming that A, B, and C are integers, and that A is not 0. The output of the program is correct, but it only gives answers that are REAL numbers, either Rational or Irrational. In particular, the QUAD1 proigram does not identify Complex Number answers. This page presents a listing of a new version of that program, called QUAD2, a version that produces nice looking output, even for Complex Number answers. The listings below are for the TI-86 version of the QUAD2 program, given in two parts.

QUAD2, part 1	QUAD2, part 2

A comparison of part 1 of the QUAD2 program with the QUAD1 program given on the earlier 208607.htm page, should confirm that the main part of the program is unchanged from one version to the other. The extra lines in QUAD2 are used to handle the case of the Complex Number answers. This is done by identifying, through examining the Discriminant, cases where the answer will be Complex, and retaining that information in the variable T. T will be used later in the program to format the output to include the imaginary number i for complex answers. Also, notice that the QUAD2 program calls (makes reference to) the TOSTR program in order to acheive a nicer looking output. TOSTR must be available on the calculator. The listing for the TOSTR program, was given on the 208604.htm page.

Naturally, one could enter the programs into a calculator. However, the TI-86 file for QUAD2 in is available at quad2.86p and the TI-86 file for TOSTR at tostr.86p. In addition, the TI-85 file for QUAD2 in is available at quad2.85p and the TI-85 file for TOSTR at tostr.85p. Depending upon your browser, you should be able to save the file to your disk and then transfer it via TI-Graphlink, assuming you have the program and the required cable.

We conclude this page with few sample runs of the TI-86 version of the QUAD2 program. We will be solving the following quadratic equations:

x² + 25 = 0
x² + 27 = 0
7x² + 31 = 0
x² - 8x + 25 = 0
x² - 4x + 67 = 0
49x² - 42x + 29 = 0

Figure 1 We open the PRGM menu by pressing the key. Then we can open the NAMES sub-menu by pressing the key. The calculator used to generate Figure 1 has many programs defined on it. We will need to use the key to shift the sub-menu until the QUAD2 program name is displayed, as it is at the bottom of Figure 2.
Figure 2 Now that the QUAD2 program name is visible in the sub-menu, we can press We will have to press the to paste that name onto the screen. Then we press the key to actually start to run the program.

Figure 3 In Figure 3 the program has started. The calculator has asked for, and we have supplied, values for the coefficients A, B, and C. We have entered the value 1 for A, 0 for B and the value 25 for C. These are the coefficients for X² + 25 = 0 The calculator is waiting for us to press to accept the value for C and to move on with the program.

Figure 4 Figure 4 shows output from the calculator. It writes the word DISCRIMINANT followed, on the next line, by the value of the discriminant. Recall that the discriminant for AX² + BX + C = 0 is B² - 4 A C In our case that is -100. Then, becuase the discriminant is negative, there will be exactly two solutions to the quadratic equation, and they will both be Complex numbers. The calculator tells us that there are two solutions, that they are complex numbers, and then it gives us the complex number solutions. In Figure 4 those values are 0+5i and 0-5i.

Figure 5 The program was completed in Figure 4. To restart it, we press . Figure 5 gives the data entry for the problem X² + 27 = 0

Figure 6 To accept our final value and continue the program we press . Figure 6 gives the result. This time the discriminant has the value -108. Because the discriminant is negative there will be two complex solutions. The program goes on to show those solutions.

Figure 7 In Figure 7 we have restarted the program by pressing the key. This time we are working on the problem 7x² + 31 = 0
We have entered the coefficients.

Figure 8 Pressing the key to accept our last input value, the program generates the information seen in Figure 8. In particular, we see that the value of the discriminant is -868, that there are two answers, that the two answers are complex, and it gives these values. Again, the program is "Done" running.

Figure 9 In Figure 9 we have restarted the program by pressing the key. This time we are working on the problem x² - 8x + 25 = 0
We have entered the coefficients.

Figure 10 Again, we press to contiue with the program. Figure 10 shows the discriminant to be -36, that there are two complex answers, and the two answers.

Figure 11 In Figure 11 we have started the program again, this time to solve the problem x² - 4x + 67 = 0

Figure 12 The program finds the discriminant, finds that there are two complex answers, gives those values.

Figure 13 In Figure 13 we have started the program again, this time to solve the problem 49x² - 42x + 29 = 0

Figure 14 We press the key to leave Figure 13 and move to Figure 14. Here we see that the value of the discriminant is -3920, and that there are two complex solutions, and we are given the values of those answers.

Figure 1	We open the PRGM menu by pressing the key. Then we can open the NAMES sub-menu by pressing the key. The calculator used to generate Figure 1 has many programs defined on it. We will need to use the key to shift the sub-menu until the QUAD2 program name is displayed, as it is at the bottom of Figure 2.
Figure 2	Now that the QUAD2 program name is visible in the sub-menu, we can press We will have to press the to paste that name onto the screen. Then we press the key to actually start to run the program.
Figure 3	In Figure 3 the program has started. The calculator has asked for, and we have supplied, values for the coefficients A, B, and C. We have entered the value 1 for A, 0 for B and the value 25 for C. These are the coefficients for X² + 25 = 0 The calculator is waiting for us to press to accept the value for C and to move on with the program.
Figure 4	Figure 4 shows output from the calculator. It writes the word DISCRIMINANT followed, on the next line, by the value of the discriminant. Recall that the discriminant for AX² + BX + C = 0 is B² - 4 A C In our case that is -100. Then, becuase the discriminant is negative, there will be exactly two solutions to the quadratic equation, and they will both be Complex numbers. The calculator tells us that there are two solutions, that they are complex numbers, and then it gives us the complex number solutions. In Figure 4 those values are 0+5i and 0-5i.
Figure 5	The program was completed in Figure 4. To restart it, we press . Figure 5 gives the data entry for the problem X² + 27 = 0
Figure 6	To accept our final value and continue the program we press . Figure 6 gives the result. This time the discriminant has the value -108. Because the discriminant is negative there will be two complex solutions. The program goes on to show those solutions.
Figure 7	In Figure 7 we have restarted the program by pressing the key. This time we are working on the problem 7x² + 31 = 0 We have entered the coefficients.
Figure 8	Pressing the key to accept our last input value, the program generates the information seen in Figure 8. In particular, we see that the value of the discriminant is -868, that there are two answers, that the two answers are complex, and it gives these values. Again, the program is "Done" running.
Figure 9	In Figure 9 we have restarted the program by pressing the key. This time we are working on the problem x² - 8x + 25 = 0 We have entered the coefficients.
Figure 10	Again, we press to contiue with the program. Figure 10 shows the discriminant to be -36, that there are two complex answers, and the two answers.
Figure 11	In Figure 11 we have started the program again, this time to solve the problem x² - 4x + 67 = 0
Figure 12	The program finds the discriminant, finds that there are two complex answers, gives those values.
Figure 13	In Figure 13 we have started the program again, this time to solve the problem 49x² - 42x + 29 = 0
Figure 14	We press the key to leave Figure 13 and move to Figure 14. Here we see that the value of the discriminant is -3920, and that there are two complex solutions, and we are given the values of those answers.